se brûler les ailes

How could I translate this French expression into an English equivalent?

"se brûler les ailes" (litterally "to burn his/her own wings") means in my context that a person while trying to achieve his goal (trying to reach the sun), is in fact losing everything because of that (burning his own wings)...

To burn one's wings is literally right. Flying too close to the sun is also right in the sense that it is a reference to Daedalus and Icarus. But maybe 'sailing too close to the wind' or 'getting one's fingers burnt' would work better depending on the context in which the expression is being used.